Sorry to be anal but with rotational dynamics it's not F=ma as it would be for an object travelling in a straight line. It would instead be Torque = moment of inertia x angular momentum. As the screwed thread is helical it is a component of the torque which acts to keep the flywheel in position before the thread rod shaft is stopped.

The nuts and bolts of the problem however is that a flywheel and threaded rod arrangement would provide a very effective means of transferring the energy to a flipper if you could engineer the individual components to survive the engagement of the flywheel.